Hillary Clinton don't see nuthin' wrong ... with a little bump 'n griiiiind ... 'cause the U.S. Secretary of State got downright FREAKY at a party in South Africa ... and it was all caught on tape.

Hillary was attending an event in Johannesburg, featuring a local band, when Hillary decided to bust out some of her moves on the dance floor ... and it's AWESOME!!

But it got WAYYY better ... when the lead singer decided to twerk all over Clinton's crotchal region.

It ain't the first time Hillary's let her hair down ... she let loose during an event in Colombia back in April ... and even pounded a beer.